# Vibrational perturbation theory (VPT2)

VPT2,options

The VPT2 program is based on force constants, which are retrieved from the polynomial coefficients as generated by the POLY program. Therefore, each VPT2 calculation requests a call of the POLY program prior to the VPT2 call. As the VPT2 program relies on a quartic force field (QFF), one may use the option TYPE=QFF in the SURF program. Once the XSURF program has been used, the directive VTAYLOR,TYPE=QFF should be called. This will lead to tremendous time savings as the size of the potential energy surface is significantly reduced. However, this is an option and the force constants can be retrieved from any potential provided by the SURF program. As the results may be sensitive to thresholds for the resonance treatment, the user may be careful concerning these. The current VPT2 implementation is limited to asymmetric top and linear molecules. For further details see:
R. Ramakrishnan, G. Rauhut, Semi-quartic force fields retrieved from multi-mode expansions: Accuracy, scaling behavior and approximations, J. Chem. Phys. 142, 154118 (2015).

The following options are available:

• COMBI=n (=0 Default) Be default only fundamental frequencies will be computed. As many applications request also overtones and combination bands, the can be computed with COMBI=1.
• DIPOLE=n DIPOLE=1 provides dipole moment surfaces to the VPT2 program and thus allows for the calculation of infrared intensities.
• DRTFREQ=value (=300.0 Default) Frequency threshold for Darling-Dennison resonances.
• DRTFC=value (=0.01 Default) Threshold for Darling-Dennison resonances concerning quartic force contants.
• FRTFREQ=value (=500.0 Default) This is the threshold for Fermi resonance detection with respect to frequencies, i.e. $2\omega_i - \omega_k$ (type 1) and $\omega_i + \omega_j - \omega_k$ (type 2).
• FRTFC=value (=0.01 Default) Threshold for Fermi resonances concerning cubic force constants (type 1 and type2).
• INFO=n INFO=1 provides a list of the values of all relevant program parameters.
• PRINT=n PRINT=0 (default) prints the anharmonic vibrational frequencies and the most important vibrational constants.

PRINT=1 prints in addition the force constants as retrieved from the polynomial coefficients.
PRINT=2 prints the force constants and an analysis of the detected resonances.

• UBOUND=value (=10000.0 Default) Upper limit of transition energies. This option can be used to limit the number of states to be computed in case of COMBI calculations.
• USERMODE=n (=0 Default) Once this keyword has been activated (USERMODE=1) the list of states to be calculated is controlled by the VIBSTATE program.

The following example shows an input for water, for which a semi-quartic force field will be generated at the MP2/cc-pVDZ level.

memory,20,m
basis=vdz
orient,mass
geometry={
3
Water
O          0.0675762564        0.0000000000       -1.3259214590
H         -0.4362118830       -0.7612267436       -1.7014971211
H         -0.4362118830        0.7612267436       -1.7014971211
}

mass,iso

hf
mp2
optg                                     !(1) optimizes the geometry
frequencies,symm=auto                    !(2) compute harmonic frequencies

label1
{hf
start,atden}
mp2

{xsurf,start1D=label1,sym=auto           !(3) generate a QFF
vtaylor,type=qff
disk,where=home,dump='water.pot'}
poly,type=qff,vam=0                      !(4) transform the PES to polynomials
vpt2                                     !(5) do a VPT2 calculation